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home / study / math / statistics and probability / statisticsand probability questions and answers / we are going to play a gameof chance. we will roll a die (half of a pair of dice) and if it... Your question has been answered Let us know if you got ahelpful answer. Rate this answer Question: We are going to play agame of chance. We will roll a die (half of a pair of dice) and ifit come... We are going to play a game of chance. We will roll adie (half of a pair of dice) and if it comes up with one or twospots showing, you win and I will pay you $1.50. If it comes upwith three, four, five, or six spots showing, you lose and you willpay me $1.00. So, the probability that you will win is 1/3 and theprobability you will lose is 2/3. What is the expected value ofthis game for you?

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3.6 Ratings (446 Votes)

EventÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Value for you (Random Variable X)Â Â Â Probability (P) of XÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â XP

Die spot:1,2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1.50Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1/3Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.50

Die spot 3,4,5,6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â - 1.00Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2/3Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â - 0.67

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Expected valueÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = - 0.17

So,

Answer is:

- 0.17

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